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(1) How is it possible and what statistical method is used when using least squares in a linear model (regression) to evaluate the correlation between multiple variables?

In my situation the program runs multiple iterations to compare multiple models and chooses the one that has the highest correlation with a ladder as comparison.

(2) When does the least square method apply here and is this a known method used in statistics ?

CONTEXT:
Fragman - DNA fragment analysis

HOW LAB DATA IS OBTAINED:
The user must supply a numeric vector containing the expected base pairs sizes of the ladder fragments co-migrating with the sample DNA fragments during capillary electrophoresis.

(TEXT):
The (FRAGMAN) program calculates the first derivative of the intensity vector for the channel of fluorescence containing the size standard, and finds the point where the slope approximates zero (where y is the intensity with respect to the index position x) using the rle function from the base package [11]. ...

... An iterative procedure using least squares creates parallel models and model with the highest correlation is then selected. ...

... This procedure confidently finds the correct fluorescent peaks in all the FSA files to match them with the expected DNA sizes of the size standard, and finally uses a linear model of the form y = Xβ + ε to assign a base pair value to each index of the intensity vector where y is the response defined as the expected DNA sizes for the ladder, X is the incidence matrix for fixed effects, β is the vector of fixed effects for the polynomial regression until the fifth order to account for the migration differential between DNA pieces of different sizes